BINOMIAL METHODS FOR BINARY MESSAGE COMPRESSION

Abstract

Two lossless numerical compression methods for binary messages using binomial coefficients are proposed. The methods are based on the decomposition of a Bernoulli source of information into a combinatorial source A and a probabilistic source B. Accordingly, the entropy of the source is also decomposed into two entropies. The entropy of source A solves the problem of enumeration encoding of compressible messages, and the entropy of source B for the first method solves the problem of optimal coding. The disadvantage of this method is the need for statistical tests. In the second method, the calculation of the maximum value of the entropy of the source B replaces the optimal encoding. This replacement avoids statistical tests, although it leads to a relatively small redundancy of compressed messages, which decreases as their length increases. The work of the methods is shown on specific examples, which allows you to better understand both the idea of the methods and their practical implementation.